What is the Cusan transformation and its significance in the history of physics?

[matheinste]

Hello all.

The following is a quote from The Routledge History of Philosophy, Vol IX, Pages 219-220.

By the end of the nineteenth century, however, it had become clear that there was a transformation under which the laws of electromagnetism were covariant. This was the Lorentz transformation. The situation had now become very interesting. The Maxwell laws of electromagnetism are covariant with respect to the transformation of Lorentz but not with respect to that of Galileo. The laws of mechanics are covariant with respect to the transformation of Galileo but not with respect to that of Lorentz. Both are covariant with respect to the Cusan trnsformation, but this was taken to be so obvious as not to be worth remarking.

What is the Cusan transformation.

Matheinste

 

[robphy]

I never heard of the Cusan transformations...
but a Google book search turned up...

from p. 116
http://books.google.com/books?id=ZlTl3UPEoT4C&pg=PA113&dq=cusa+relativity&lr=#PPA116,M1

From Cusa we have a principle of the indifference of the unfolding of
material processes to the place or moment at which they occur. From
Galileo we have a principle of the indifference of the unfolding of mechanical
processes to their velocity relative to any unobservable background,
of which absolute space, time and space-time would be cases. Finally
from Einstein we have a conceptual demonstration of the indifference of
all physical processes, mechanical and electromagnetic, to their relative
velocity to some alleged absolute material background, the aether.

Each level of indifference can be expressed as a principle of covariance,
in that the laws of nature describing physical processes take the
same form under progressively more restrictive coordinate transformations.
Displaying the development of relativistic physics as a progressively
more stringent application of the covariance requirement involves,
in a queer way, the retention of the absolutist concepts for the exposition
of relativity. We set up the progressively tighter relativity 'theories' by
affirming, step by step, 'No change in the laws of nature with respect to
changes in absolute positions, moments or motions, in an imagined
basic manifold or set of manifolds.' Expressing the laws of nature in such
forms as meet the covariance conditions for each level of stringency we
can then safely ignore such absolutes in physics. We can throw away
the ladder once we have ascended it! Making the totality of the laws
of physics, mechanics, electromagnetism, quantum mechanics and so on
covariant under the Lorentz transformation, is just to make them independent
of the most general candidate for an absolute spatio-temporal
manifold, the Minkowski space-time.

Mould, Basic Relativity makes reference to Nicholas of Cusa on p.3.

Relativity as a general philosophical idea can be found wherever one
finds philosophy. Probably the first to express it as a physical idea
in the Christian Era was Nicholas of Cusa, a cardinal of the Roman
Catholic Church and contemporary of Leonardo da Vinci. Unlike Aristotle,
Cusa accepted the idea of relativity of motion and rejected the
medieval notion that there are special directions in space such as up to
Heaven or down to Hell. Cusa's universe was an endless homogeneous
and isotropic space occupied only by many beautiful stars in relative
motion. He believed that an observer looking at the Earth from the
Sun would see it as another shining star.' Not only did Cusa's ideas
foreshadow relativity, but the cosmological principle as well.

 

[matheinste]

Thanks for your reply robphy.

I found references to the cardinal but none to the transform. It is strange that, although the quote from the Routledge History of Philosophy seems to assume that the reader requires no explanation because he or she will have some knowledge of it, it turns out to be so elusive.

Matheinste.

 

[matheinste]

Hello all.

For anyone interested i think i can answer my own question. Re reading part of the quoted book i found that it implies, without exactly stating, that the Cusan transformation is merely a change of position in space, a shift.

Matheinste.

 

[robphy]

Hello all.

For anyone interested i think i can answer my own question. Re reading part of the quoted book i found that it implies, without exactly stating, that the Cusan transformation is merely a change of position in space, a shift.

Matheinste.

Can you specify a particular section in that reference?

 

[matheinste]

Hello robphy

Here is the reference. I have copied out the relevant paragraph in full for anyone interested who does not have access to the book.

The Routledge History of Philosophy, Vol IX, Chapter 6-The Philosophy of Physics. Page 218.

:- If a law of physics has the same form before and after the transformation is applied to the coordinates, we say that it is 'covariant under the transformation'. However, the technical idea is a version of a more fundamental conception. It expresses the idea that the forms of the laws of nature are indifferent to (that is unaffected by ) changes in location, epoch or relative velocity of the frame with respect to which they are studied. We can detect the very beginnings of the covariance or indifference to location idea in the writings of Nicholas of Cusa. Contrary to the Aristotleans, who believed that space and time had intrinsic structures, the laws of nature differing with the location in which they are studied within the structure, Cusa introduced a general principle of indifference. His elegant epigram ran as follows:- 'the centre and circumference of the universe are the same', or in other words, physical laws are indifferent to their location in space and also, he believed, in time.

Matheinste.